It is important to distinguish between axioms (things you assume), definitions and theorem (things you prove from axioms, stated in terms of definitions). So,

It is important to distinguish between axioms (things you assume), definitions and theorem (things you prove from axioms, stated in terms of definitions). So, for basic arithmetic, your assumptions might be the defining properties of numbers: associativity, distributivity, etc. In this setting, 1 + 1 = 2 is basically a definition, while (-1)* (-1) = 1 is something to be proved: 0 = 0* (-1) (0* x = 0 for all x) = (1 + (-1))* (-1) (x + -x = 0) = 1* (-1) + (-1)* (-1) (distributivity) = (-1) + (-1)* (-1) (1* x = x for all x) implies: 1 = (-1)* (-1) (equality; add 1 to both sides) Finally, slope = rise/run is a definition. It is not something you "see" to be true. So assumption vs. definition vs. theorem can explain part of it. Another part is familiarity. 1 + 1 = 2 is ubiquitous in daily life. Depending on what you think about, (-1)* (-1) = 1 may not be. You probably have lots of interpretations of 1 + 1 = 2 (counting, number line, shopping, money, etc.) How many such interpretations of (-1)* (-1) = 1 do you have? I highly recommend this book, written by two mathematicians: http://www.amazon.com/5-Elements-Effective-Thinking-ebook/dp/B008JUVDUE/ref=sr_1_1?s=books&ie=UTF8&qid=1423244565&sr=1-1&keywords=5+elements+effective+thinking http://www.amazon.com/5-Elements-Effective-Thinking-ebook/dp... It's now about mathematics per se, but about learning how to learn and think better. Good luck.